Problem 1 SUBSTITUTION: y=12x-3 y=5x+2 Step 1:To solve this problem is fairly simple. The first step that must be taken is getting y alone. In this problem it has already been done for us. Step 2: We must now plug y into the other equation (12x-3)=5x+2 Step 3: solve for x (12x-3)=5x+2 12x-3=5x+2 -5x -5x ---------------- 7x-3=2 -3 -3 --------------- 7x=-1 /7 /7 x=-.142 Step 4: Now plug x into the other equation y=12(.142)-3 Step 5: Solve for Y y=12(.142)-3 y=1.704-3 y=-1.29 Step 6: Y=-1.29 X=-.142 Problem 2 Elimination: y=4-1x Y=2+1x Step 1: The first step to solving a problem in Elimination is you must first have a part of both problems that are opposite, This is done for you already in this problem, then they cancel each other out. y=4-1x y=2+1x Step 2: Subtract both Xs of the problem by each other. y=4 y=2 ---------- y=2 Step 3: Plug in Y into the any beginning equation (2)=4-1x Step 4: Solve 2=4-1x -4 -4 ----------- -2=-1x 2=x Step 4: y=2 x=2 Word problem:The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? Step 1: Find the variables; the first step to a word problem is to find the variables Amount of adults: A Amount of Children:C Step 2: Make two equations for the problem: Amount of people coming: a + c = 2200 total income : 4a + 1.5c = 5050 Step 3: Solve like a normal problem. (you can use either substitution or elimination, in this case we will substitution) Step 4: get one variable by itself 4a + 1.5c = 5050 a + c = 2200 -c -c ----------------- a=2200-c Step 5: Substitute into other equation 4(2200-c) + 1.5c = 5050 8800-4c+1.5c=5050 -8800 -8800 ------------------------------ -4c+1.5c=-3750 -2.5c=-3750 /-2.5 /-2.5 ------------------- c=1500 Step 6: Plug The variable into either equation 4a + 1.5(1500) = 5050 Step 7: Solve 4a + 1.5(1500) = 5050 4a+2250=5050 -2250 -2250 ------------------------------- 4a=2800 /4 /4 a=700 Step 8: Plug back into the word problem 1500 children and 700 adults Sat problem: will be doing it Elimination. If 7x + y = 25 and 6x + y = 23, what is the value of x? Step 1: This is the type of question that will be on a SAT. They give a specific question that is asked in the problem but not the whole answer. In this question, they ask for X value, which will go exactly the same as any other problem. Step 2: Make One variable the opposite of each other. 6x + y = 23 7x + y = 25 into 6x+y=23 -7x-y=-25 Step 3: get rid of the opposite variable, add the two problems from each other. 6x=23 -7x=-25 ------------- -1x=-2 Step 4: solve x=2
Geometry problem: You work for a fencing company. A customer called this morning, wanting to fence in his 1,320 square-foot garden. He ordered 148 feet of fencing, but you forgot to ask him for the width and length of the garden. Because he wants a nicer grade of fence along the narrow street-facing side of his plot, these dimensions will determine some of the details of the order, so you do need the information. But you don't want the customer to think that you're an idiot, so you need to figure out the length and width from the information the customer has already given you. What are the dimensions? Step 1: Identify variables. width=W length L Step 2: Make the Two equations that are given in the word/ geometry problem. L + W = 74 L×W = 1320 Step 3: Get a variable by itself. L+W=74 -W -W -------------- L=74-W Step 4: Substitute into the other equation. (74-W) x W=1320 74W– W 2 = 1320 0 = W 2 – 74W + 1320 0 = (W – 30)(W – 44) Step 5: Plug in the answers to the word problem. W = 30 or W = 44 Step 6: Relate it and connect it back to words of the word problem. The measurements of the garden are 44 feet by 30 feet.
Lukas' Reflection-
The first study habit that I would like to include for geometry next year is to just review the standards the night before I take the test. The second study habit I would include is that do all your in class work because that boosts my grade by a lot. And the last study habit that I would like to include in next years geometry is to not listen to music while in class because it takes away from my learning. A tip that I would give to an incoming freshman would be to really just put yourself to work because it will pay off in the end and your are investing in your future. And the second tip would be that get on the good side of teachers because maybe they will cut you some slack.
Problem 1 SUBSTITUTION: y=12x-3
y=5x+2
Step 1:To solve this problem is fairly simple. The first step that must be taken is getting y alone. In this problem it has already been done for us.
Step 2: We must now plug y into the other equation
(12x-3)=5x+2
Step 3: solve for x
(12x-3)=5x+2
12x-3=5x+2
-5x -5x
----------------
7x-3=2
-3 -3
---------------
7x=-1
/7 /7
x=-.142
Step 4: Now plug x into the other equation
y=12(.142)-3
Step 5: Solve for Y
y=12(.142)-3
y=1.704-3
y=-1.29
Step 6: Y=-1.29
X=-.142
Problem 2 Elimination: y=4-1x
Y=2+1x
Step 1: The first step to solving a problem in Elimination is you must first have a part of both problems that are opposite, This is done for you already in this problem, then they cancel each other out.
y=4-1x
y=2+1x
Step 2: Subtract both Xs of the problem by each other.
y=4
y=2
----------
y=2
Step 3: Plug in Y into the any beginning equation
(2)=4-1x
Step 4: Solve
2=4-1x
-4 -4
-----------
-2=-1x
2=x
Step 4: y=2 x=2
Word problem:The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
Step 1: Find the variables; the first step to a word problem is to find the variables
Amount of adults: A Amount of Children:C
Step 2: Make two equations for the problem:
Amount of people coming: a + c = 2200
total income : 4a + 1.5c = 5050
Step 3: Solve like a normal problem. (you can use either substitution or elimination, in this case we will substitution)
Step 4: get one variable by itself
4a + 1.5c = 5050
a + c = 2200
-c -c
-----------------
a=2200-c
Step 5: Substitute into other equation
4(2200-c) + 1.5c = 5050
8800-4c+1.5c=5050
-8800 -8800
------------------------------
-4c+1.5c=-3750
-2.5c=-3750
/-2.5 /-2.5
-------------------
c=1500
Step 6: Plug The variable into either equation
4a + 1.5(1500) = 5050
Step 7: Solve
4a + 1.5(1500) = 5050
4a+2250=5050
-2250 -2250
-------------------------------
4a=2800
/4 /4
a=700
Step 8: Plug back into the word problem
1500 children and 700 adults
Sat problem: will be doing it Elimination.
If 7x + y = 25 and 6x + y = 23, what is the value of x?
Step 1: This is the type of question that will be on a SAT. They give a specific question that is asked in the problem but not the whole answer. In this question, they ask for X value, which will go exactly the same as any other problem.
Step 2: Make One variable the opposite of each other.
6x + y = 23
7x + y = 25
into
6x+y=23
-7x-y=-25
Step 3: get rid of the opposite variable, add the two problems from each other.
6x=23
-7x=-25
-------------
-1x=-2
Step 4: solve
x=2
Geometry problem: You work for a fencing company. A customer called this morning, wanting to fence in his 1,320 square-foot garden. He ordered 148 feet of fencing, but you forgot to ask him for the width and length of the garden. Because he wants a nicer grade of fence along the narrow street-facing side of his plot, these dimensions will determine some of the details of the order, so you do need the information. But you don't want the customer to think that you're an idiot, so you need to figure out the length and width from the information the customer has already given you. What are the dimensions?
Step 1: Identify variables.
width=W
length L
Step 2: Make the Two equations that are given in the word/ geometry problem.
L + W = 74
L×W = 1320
Step 3: Get a variable by itself.
L+W=74
-W -W
--------------
L=74-W
Step 4: Substitute into the other equation.
(74-W) x W=1320
74W– W 2 = 1320
0 = W 2 – 74W + 1320
0 = (W – 30)(W – 44)
Step 5: Plug in the answers to the word problem.
W = 30 or W = 44
Step 6: Relate it and connect it back to words of the word problem.
The measurements of the garden are 44 feet by 30 feet.
Lukas' Reflection-
The first study habit that I would like to include for geometry next year is to just review the standards the night before I take the test. The second study habit I would include is that do all your in class work because that boosts my grade by a lot. And the last study habit that I would like to include in next years geometry is to not listen to music while in class because it takes away from my learning. A tip that I would give to an incoming freshman would be to really just put yourself to work because it will pay off in the end and your are investing in your future. And the second tip would be that get on the good side of teachers because maybe they will cut you some slack.